Emergence of event cascades in inhomogeneous networks

Nondifferentiable activity in the brain

Spike raster plots of numerous neurons show vertical stripes, indicating that neurons exhibit synchronous activity in the brain. We seek to determine whether these coherent dynamics are caused by smooth brainwave activity or by something else. By analyzing biological data, we find that their cross-correlograms exhibit not only slow undulation but also a cusp at the origin, in addition to possible signs of monosynaptic connectivity. Here we show that undulation emerges if neurons are subject to smooth brainwave oscillations while a cusp results from nondifferentiable fluctuations. While modern analysis methods have achieved good connectivity estimation by adapting the models to slow undulation, they still make false inferences due to the cusp. We devise a new analysis method that may solve both problems. We also demonstrate that oscillations and nondifferentiable fluctuations may emerge in simulations of large-scale neural networks.

Simulating emergence of novelties using agent-based models

Understanding the growth and evolution of social networks is an important area of study, as these networks form the foundation for many popular online services such as social networking sites (SNS) and online games. However, previous models developed to explain the growth mechanisms of these networks have struggled to accurately reproduce certain behaviors that are frequently observed in real data, such as waves of novelty, in which new individuals or topics receive more attention than existing ones for a short period of time. In this study, we introduce a new model that incorporates context information into existing agent-based models in order to more accurately capture the structure and growth dynamics of these networks. Context information is introduced through labels based on the timing of appearance and relationships with antecedent agents. New agents are first added to the network when they are called by existing agents, and at this time they are also given a label. Agents added to the network at the same time by the same agent will have the same label. These labels are used to classify agents and give them different selection probabilities. This newly introduced selection probability creates a mechanism in which new agents receive attention beyond preferential attachment. By comparing the results of our model with real data on ten metrics, we demonstrate that it is able to produce behavior that more closely resembles real data. This improved understanding of the dynamics of social networks has important implications for designing effective interventions, including strategies for user acquisition and retention.

Estimating the time-varying reproduction number of COVID-19 with a state-space method

After slowing down the spread of the novel coronavirus COVID-19, many countries have started to relax their confinement measures in the face of critical damage to socioeconomic structures. At this stage, it is desirable to monitor the degree to which political measures or social affairs have exerted influence on the spread of disease. Though it is difficult to trace back individual transmission of infections whose incubation periods are long and highly variable, estimating the average spreading rate is possible if a proper mathematical model can be devised to analyze daily event-occurrences. To render an accurate assessment, we have devised a state-space method for fitting a discrete-time variant of the Hawkes process to a given dataset of daily confirmed cases. The proposed method detects changes occurring in each country and assesses the impact of social events in terms of the temporally varying reproduction number, which corresponds to the average number of cases directly caused by a single infected case. Moreover, the proposed method can be used to predict the possible consequences of alternative political measures. This information can serve as a reference for behavioral guidelines that should be adopted according to the varying risk of infection.